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A233129 T(n,k) = number of n X k 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabeled 6-colorings with no clashing color pairs).

%I A233129 #8 Sep 12 2024 19:36:17
%S A233129 1,1,1,3,8,3,10,80,80,10,36,896,2688,896,36,136,10496,96256,96256,
%T A233129 10496,136,528,124928,3497984,10674176,3497984,124928,528,2080,
%U A233129 1495040,127533056,1189609472,1189609472,127533056,1495040,2080,8256,17924096
%N A233129 T(n,k) = number of n X k 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabeled 6-colorings with no clashing color pairs).
%C A233129 Table starts
%C A233129 .....1..........1...............3...................10
%C A233129 .....1..........8..............80..................896
%C A233129 .....3.........80............2688................96256
%C A233129 ....10........896...........96256.............10674176
%C A233129 ....36......10496.........3497984...........1189609472
%C A233129 ...136.....124928.......127533056.........132682612736
%C A233129 ...528....1495040......4653056000.......14800557965312
%C A233129 ..2080...17924096....169793814528.....1651015493353472
%C A233129 ..8256..215023616...6196127858688...184172904936636416
%C A233129 .32896.2580021248.226111237652480.20544737466392772608
%H A233129 R. H. Hardin, <a href="/A233129/b233129.txt">Table of n, a(n) for n = 1..364</a>
%F A233129 Empirical for column k:
%F A233129 k=1: a(n) = 6*a(n-1) -8*a(n-2) for n>3
%F A233129 k=2: a(n) = 16*a(n-1) -48*a(n-2)
%F A233129 k=3: a(n) = 48*a(n-1) -448*a(n-2) +1024*a(n-3)
%F A233129 k=4: a(n) = 160*a(n-1) -6144*a(n-2) +86016*a(n-3) -393216*a(n-4)
%F A233129 k=5: [order 6]
%F A233129 k=6: [order 8]
%F A233129 k=7: [order 14]
%F A233129 Empirical for row n:
%F A233129 n=1: a(n) = 6*a(n-1) -8*a(n-2) for n>3
%F A233129 n=2: a(n) = 16*a(n-1) -48*a(n-2)
%F A233129 n=3: a(n) = 48*a(n-1) -448*a(n-2) +1024*a(n-3)
%F A233129 n=4: a(n) = 160*a(n-1) -6144*a(n-2) +86016*a(n-3) -393216*a(n-4)
%F A233129 n=5: [order 6]
%F A233129 n=6: [order 8]
%F A233129 n=7: [order 14]
%e A233129 Some solutions for n=3 k=4
%e A233129 ..0..1..0..1....0..1..5..2....0..1..2..4....0..1..5..4....0..1..0..4
%e A233129 ..4..5..1..2....2..0..2..1....1..2..4..5....2..5..2..5....2..5..3..0
%e A233129 ..5..4..0..4....4..3..5..3....2..1..2..4....0..3..0..4....0..3..0..2
%Y A233129 Column 1 is A007582(n-2).
%K A233129 nonn,tabl
%O A233129 1,4
%A A233129 _R. H. Hardin_, Dec 04 2013